SOLUTION: Hey, could you please help me in one of my questions.. I am in year 11 and im struggling on this question. ABCDEFGH is a regular octagon. BCKFGJ is a hexagon. JK is a line of

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Question 1025760: Hey, could you please help me in one of my questions.. I am in year 11 and im struggling on this question.
ABCDEFGH is a regular octagon.
BCKFGJ is a hexagon.
JK is a line of symmetry of the hexagon.
Angle BJG = angle CKF = 140q
Work out the size of angle KFE.
You must show all your working
The Link to this question is http://revisionmaths.com/sites/mathsrevision.net/files/imce/Questionpaper-Paper1H-November2014.pdf
Its Question 1 On the Exam paper^^ Thanks for the help
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the interior angles of a regular octagon are 135 degrees each.

since JK is a line of symmetry, this means that CK = KF.

draw the line CF and you have an isosceles triangle.

this means that angle KCF and KVC are each 20 degrees.

this is because the sum of the angles of a triangle are 180 degrees.

140 + 2 * 20 = 180 degrees.

you have the following:

angle KFC = 20 degrees.

angle CFG = 90 degrees.

this means that angle KFG = 90 + 20 = 110 degrees.

since angle EFG = 135 degrees and angle KFG = 110 degrees, this means that angle EFK must be equal to 25 degrees.

that's your solution.

angle KFE is equal to 25 degrees.

the following diagram shows this relationship.

it's all there except i didn't draw in line JK.